The Legendre Equation. 22 through 29 deal with the Legendre8 equation (1 x2 )y 2xy + ( +

Chapter 5, Problem 22

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The Legendre Equation. 22 through 29 deal with the Legendre8 equation (1 x2 )y 2xy + ( + 1)y = 0. As indicated in Example 3, the point x = 0 is an ordinary point of this equation, and the distance from the origin to the nearest zero of P(x) = 1 x2 is 1. Hence the radius of convergence of series solutions about x = 0 is at least 1. Also notice that we need to consider only > 1 because if 1, then the substitution = (1 + ), where 0, leads to the Legendre equation (1 x2)y 2xy + ( + 1)y = 0.

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